Unit 6 reviews and builds on children's understanding of comparing numbers. Children are introduced to picture graphs, tables, and calibrated units. Use of these graphic representations helps children see information in a way that makes comparisons clear and visual. Throughout the unit, children discuss relationships such as how many more, how many less, and how two amounts can be made equal. As they articulate the relationships between the various amounts they see, they develop precision in mathematical expression. A fundamental idea in kindergarten through grade 2 is that data can be organized or ordered and that this "picture" of the data provides information about the phenomenon or question. As children begin to understand ways of representing data, they will be ready to compare two or more sets.

Picture Graphs
The earliest picture graphs in Unit 6 contain only two rows of symbols. Children are asked to make the two quantities equal. This approach helps them to see the difference. It also helps them develop the double focus that is necessary for drawing comparisons: the first amount is x units more than the second, and the second amount is x units fewer than the first. When children proceed to picture graphs with three or four rows, another set of skills comes into play. Here children are asked to find the greatest or least quantity on the graph as they learn to make general comparisons rather than restricted comparisons. They are also learning to select relevant information-- another valuable skill.

Story Problems with Comparisons Daniel has 6 apples. Abby has 4 apples. How many more apples does Daniel have than Abby?
The language of comparing and equalizing can be particularly troublesome for young children. The question in a problem such as the one above actually requires three questions to be answered: How many apples does Daniel have? How many apples does Abby have? What is the difference? The use of picture graphs and Stair Steps helps children focus on each of these questions one at a time. Children can also make math drawings and match Daniel's apples to Abby's apples.

Measurement
In conjunction with comparison and equalizing story problems, children are introduced to simple measurement increments involving drawings of inch rulers. At this point, they are not expected to position the ruler themselves, only to observe the results. These measurement calibrations provide them with another context for exploring comparisons.

Picture GraphsThe earliest picture graphs in Unit 6 contain only two rows of symbols. Children are asked to make the two quantities equal. This approach helps them to see the difference. It also helps them develop the double focus that is necessary for drawing comparisons: the first amount is

xunits more than the second, and the second amount isxunits fewer than the first. When children proceed to picture graphs with three or four rows, another set of skills comes into play. Here children are asked to find the greatest or least quantity on the graph as they learn to make general comparisons rather than restricted comparisons. They are also learning to select relevant information-- another valuable skill.Story Problems with ComparisonsDaniel has 6 apples. Abby has 4 apples. How many more apples does Daniel have than Abby?The language of comparing and equalizing can be particularly troublesome for young children. The question in a problem such as the one above actually requires three questions to be answered: How many apples does Daniel have? How many apples does Abby have? What is the difference? The use of picture graphs and Stair Steps helps children focus on each of these questions one at a time. Children can also make math drawings and match Daniel's apples to Abby's apples.

MeasurementIn conjunction with comparison and equalizing story problems, children are introduced to simple measurement increments involving drawings of inch rulers. At this point, they are not expected to position the ruler themselves, only to observe the results. These measurement calibrations provide them with another context for exploring comparisons.

Fuson, Karen,

Math Expressions, Unit 6 Overview